: : : : The version of "eeny, meeny,
miny, moe" that was current in playgrounds when I was a child (1960's Britain),
replaced the word "tiger" with "nigger". This is of course totally unacceptable
by today's standards, given the massively pejorative and racist overtones that
the word has gained over the ensuing years. At the time, however, it was used
in total innocence.

: : : The "n____" version was current among U.S. children
in the 1950s. As I understand it, the word hasn't gained racist overtones since
then: it had them all the time. No, that's not strong enough. Not just overtones.
The whole meaning of the word was just plain racist. What has changed is people's
sensibilities about racism--including the words that help to perpetuate it. (In
the U.S., we had a civil rights movement that got national attention inthe 1960s,
followed by other changes in the culture.)
: : : There were more lyrics. The
next verse started "If he hollers (or another verb here?), make him pay / Fifty
dollars every day." I don't remember the rest. It might be in a book I don't have,
Iona and Peter Opie, "The Lore and Language of Schoolchildren."

: : Try the
link below (http://instruct.uwo.ca/english/133e-scor/nr.html). That page says
the chant, in some form, may go back to Druidic sacrifices of children. Another
site I found says the old British version had "catch a tinker" and the "n____"
version may date only to the beginning of World War II, when GIs arrived in England.

:
The Druidic comment above is interesting, because I've also heard that (but had
forgotten). The Druids were around in Britain before the advent of written language
here as far as I am aware - so approximately up to two thousand years ago, with
the advent of the Romans starting the downfall of native British Druidic culture.

:
Given that there are no writings to study from those times, I wonder if anyone
knows the Gaelic for "one, two, three, four" or possibly the modern Irish or Welsh?

Or,
one, two, three, four. This is the Scotch Gaelic variant. The Irish is very similar.